A two-stage phase II clinical trial design with nested criteria for early stopping and efficacy

Abstract

We propose a two-stage design for a single arm clinical trial with an early stopping rule for futility. This design employs different endpoints to assess early stopping and efficacy. The early stopping rule is based on a criteria determined more quickly than that for efficacy. These separate criteria are also nested in the sense that efficacy is a special case of, but usually not identical to, the early stopping endpoint. The design readily allows for planning in terms of statistical significance, power, expected sample size, and expected duration. This method is illustrated with a phase II design comparing rates of disease progression in elderly patients treated for lung cancer to rates found using a historical control. In this example, the early stopping rule is based on the number of patients who exhibit progression-free survival (PFS) at 2 months post treatment follow-up. Efficacy is judged by the number of patients who have PFS at 6 months. We demonstrate our design has expected sample size and power comparable with the Simon two-stage design but exhibits shorter expected duration under a range of useful parameter values.

Keywords: curtailed sampling; expected sample size; expected trial duration; minimax design.

FIGURE 1

Graphical schematic of notation for follow-up times, numbers of patients enrolled, outcome classifications, and their binomial probabilities. At the conclusion of stage 1 at follow-up time t₁, there are X₁ successes, and we need a minimum of r₁ of these to continue to stage 2. At follow-up time t₂, there are X₁₂+X₂ successes, and we need a minimum of r₂ of these to reject the null hypothesis

FIGURE 2

Probability of rejecting the null hypothesis for the nested minmax/optimal design “A” in Table 1 for the lung cancer example. The locations of the null and alternative hypotheses are indicated

FIGURE 3

Expected trial duration in a planned trial described in section 5 using the optimal nested design “A” (solid line), Simon optimal (dash), and Simon minimax (dots) using curtailed sampling for different values of the efficacy parameter p₂ and accrual rates λ.